Here are in details all the levels that the Saiyans can reach!
From the "simple" Super Saiyan to the Super Saiyan IV... through several intermediate steps. Of course, there are also the descriptions of the "Saiyan Basic Model" and of the Ohzaru, that is just hinted since there is a special section dedicated to it!



Saiyan

Coming from Planet Vegeta, the Saiyans are a warrior race having different characteristics: black hair having always the same shape and length, tail, aggressive attitude and infinite appetite. Since they are not very clever, they exploit their victims technology (as that of Tsufurus)... they are always looking for new world to conquer ( and resell). They are very strong and, when they recover after deadly wounds, their power increases... this ability is called Zenkai Power and there is a special section about it!



Half-breed Saiyan

The Saiyans born on Earth are of course half-breed, since in them there are also their Eartling mothers' blood. But it seems that the union of these two races results in some very powerful beings, maybe even more powerful than pure Saiyans. Goten and Trunks are able to turn Super Saiyan when they are still little kids, while Gohan can even control himself when he is turned Ohzaru, although he never did any special training.
Hal-breed Saiyan are: Son Gohan, Son Goten, Trunks, Bra and Pan.



Ohzaru

Saiyans can turn Ozharu when they look to a full moon. Their strength and energy increase 10 times, but everything depends on the tail: in fact, if this one is missed, the transformation cannot take place. Not all the Saiyans can control themselves when they turn Ohzaru... Goku, for exempla, completely loses consciousness!
The ones who reach this level are: Bardock, Son Goku, Son Gohan and Vegeta (and all the other Saiyans with tail).



Super Saiyan

An ancient legend tells that every 1000 years a special Saiyan born, having a huge power, called Super Saiyan. The first one who reaches this level is Goku, during the battle against Freeza, but then also the other Saiyans will reach it. The transformation into Super Saiyan is due to the rage that, exploding, makes the changing: the hair stands on end and become blond like the eyebrows, while the eyes turn green.
The ones who reach this level are: Son Goku, Future Trunks, Vegeta, Son Gohan, Broly, Goten, Trunks, Vegeth, Gotenks and Gogeta.



Super Saiyan Dai Ni Dankai

Literally "the great Super Saiyan of second level"... This level is characterized by an increasing of the muscles that can take advantages as long as is not reached the following level. The first who reaches this level is Vegeta in the room of Spirit and Time.
The ones who reach this level are: Son Goku, Vegeta and Trunks.



Super Saiyan Dai San Dankai

Literally "the great Super Saiyan of third level". As is written above, this level can present some troubles... in fact, the muscles have increased so much that the entire body has been deformed, causing the speed to reduce. It's Trunks who learns it to his cost, during the fight against Cell... the boy is sure to win 'till Cell makes him notice that strength is nothing without speed! Goku and Vegeta notice of the lack of this level and so neither one of them will use it. Broly (but please note that in this case we talk about a movie character!) is actually the only one who will keep moving fast using this level!
The ones who reach this level are: Son Goku, Vegeta, Future Trunks and Broly.



Super Saiyan Full Power

This is the utmost power level that a Super Saiyan can reach. SSJ Full Power looks just like a Super Saiyan, but he's incredibly calm and can maintain this transformation as long as he wants. Goten and Trunks have this ability since their birth.
The ones who reach this level are: Son Goku, Son Gohan, Vegeta, Son Goten and Trunks.



Super Saiyan II

This level is reached for the first time by Son Gohan, during the Cell Games. Gohan, pushed by Cell, lets himself completely go and the transformation takes place. His power increases drastically as his arrogance, the hair stands on end even more and his body is surrounded by lightnings.
Goku reaches this level in the other world, after the Cell Games, Vegeta, instead, during the Majin Buu saga, when he's under Babidi control.
The ones who reach this level are: Son Goku, Son Gohan, Vegeta and Vegeth.



Super Saiyan III

Goku reaches this level in the other world and we see it for the first time during the fight against Fat Majin Buu. His hair is still blond, but this time they are very long while his eyebrows disappear. Also Gotenks, the fusion between Goten and Trunks, is able to reach this level during the training in the room of Spirit and Time.
The ones who reach this level are: Son Goku and Gotenks.



Saikyou No Senshi

This level is reached by Gohan after he has been strengthened by the Old Kaiohshin jumped out from the Z Sword. The Americans call him "Mystic Gohan", but the translation should be "Final Warrior". This level has not any physical mutation (hair, eye...) but Saikyou No Senshi is as powerful than a Super Saiyan III.



Ohzaru Gold

It's preatty much like the normal Ohzaru... but his hair is golden! This level is reached for the first time by Goku during the fight against Baby-Vegeta on Planet Plant. Also for this transformation the tail is required; that's for this reason that and Baby-Vegeta and Vegeta (who do not have the tail anymore) reach this level just thanks to the device made by Bulma.
The ones who reach this level are: Son Goku, Baby-Vegeta and Vegeta.



Super Saiyan IV

After he has turned Ohzaru Gold, Goku recovers his self control and his aspect returns "human": long black, hair, red hairs on his body and bloodshot eye... it's the Super Saiyan IV.
During the fight against Super Ishinlon, Vegeta will reach this level too, and will unite to Goku using the Fusion, giving birth to Gogeta Super Saiyan 4... the most powerful warrior in the whole Universe!
The ones who reach this level are: Son Goku, Vegeta and Gogeta.